Sessions

  • Speaker Time Recommendations:
    • Invited Speakers: 25–30 minutes.
    • Contributing Speakers: 15–20 minutes.
  • Presentation Limit: Participants are encouraged to limit their presentations to a maximum of two per session to maintain engagement.
1. Advances in Nonlinear Analysis
  • Organizer: Monica Musso and Berikbol T. Torebek
  • Description: This session will discuss recent original research related to nonlinear analysis, partial differential equations and their possible applications.
2. Analysis and Mathematical Finance
  • Organizer: Yerkin Kitapbayev and Jorge P. Zubelli
  • Description: This session will concentrate on the recent applications of analysis to important problems in mathematical finance. Specifically, we will explore the application of advancements in partial differential equations (elliptic and parabolic), inverse problems, and integral equations. Examples of these applications in finance encompass options pricing, portfolio optimization problems, optimal transport, mean-field games, and various others.
3. Application of Dynamical Systems Theory in Biology
  • Organizer: Torsten Lindström
  • Description: In this session we accept primarily talks that are using dynamical systems theory in order to analyze various models that arise in biological applications. The models analyzed may be mechanistically formulated, fitted to data, deterministic, or stochastic. Various relations between such models that arise in different modeling approaches and under different simplifying assumptions can be analyzed. Possible biological applications can include ecology, epidemiology, pharmacokinetics, evolution, physiology, pattern formation, and resource distribution, but are not limited to these topics. A part of the session is reserved for stakeholders with rich contact networks outside academia.
4. Beyond Nodes and Edges: The Power of Complex Networks in Modeling Real-World Systems
  • Organizers: Ardak Kashkynbayev, Rakkiyappan Rajan, Balachandran Manavalan, and Jinde Cao
  • Description: Complex networks are systems with many interconnected components exhibiting emergent behaviors. One intriguing phenomenon is synchronization, where nodes coordinate their behavior over time. The network topology, node dynamics, and coupling strength influence synchronization patterns. Studying synchronization provides insights into organizing principles of complex systems and has applications across domains like neuroscience, power grids, and communication networks. This session invites all presentations related to the topic.
5. Classical Fourier Analysis
  • Organizers: Erlan Nursultanov, Sergey Tikhonov, Dauren Bazarkhanov, Egor Kosov
  • Description: The session will focus on the classical problems in Fourier analysis such as convergence of Fourier series/transforms, Fouirer inequalities, as well as interplay with function spaces and approximation theory. Particular attention will be given to function spaces that arise in the context of these problems. This session is dedicated to the 70th anniversary of Professor Mikhail Dyachenko.
6. Complex Analysis and Partial Differential Equations
  • Organizers: Okay Celebi, Sergei Rogosin, and Carmen Judith Vanegas
  • Description: This session focus primarily on theory of complex analysis and convex optimization and their applications in wave physics. Complex analysis in one or several variables is considered as well as convex or non-convex optimization. Typical research areas include the various representation theorems and moment problems involving Herglotz-Nevanlinna and Stieltjes functions and their applications to linear, time translational invariant, causal, and passive systems to derive performance bounds in wave physics. Optimization can be used to analyze the realizability of performance bounds, and for automated design of acoustic or electromagnetic structures. Other research areas involving complex analysis and convex or non-convex optimization are also highly appreciated.
7. Complex Variables and Potential Theory
  • Organizers: Tahir Aliyev Azeroglu, Massimo Lanza de Cristoforis, Anatoly Golberg, and Sergiy Plaksa
  • Description: This session is devoted to the wide range of directions of complex analysis, potential theory, their applications and related topics.
8. Computational and Applied Mathematics
  • Organizers: Nurlan Temirbekov, Bakytzhan Zhumagulov, Bolatbek Rysbaiuly, Almas Temirbekov, Dossan Baigereyev, Dinara Tamabay
  • Description: The issues of approximation, stability and convergence of finite-difference, variational-difference and projection-difference schemes for the Navier-Stokes equations in the velocity-pressure and current-vortex velocity variables will be discussed.  There will be talks on the following computational methods for solving the Navier-Stokes equations in domains with complex geometry:
    – method of curvilinear coordinates and adaptive curvilinear grids,
    – method of fictitious domains with continuation by minor and major coefficients,
    – modeling of boundary conditions for pressure and total head,
    – method of fictitious domains using variational technique,
    – finite element method.
    Discussion of a new formulation of the problem of optimizing the size of the auxiliary domain in the method of fictitious domains.
    New formulations and methods for solving direct and inverse problems of mathematical geophysics and environmental protection will be discussed. Issues of joint use of mathematical models and observation data by the variational data assimilation technique will be considered.
9. Constructive Methods in Boundary Value Problems and Applications
  • Organizer:  Vladimir Mityushev, Gia Giorgadze, and Piotr Drygaś
  • Description: This session is devoted to boundary value problems and their practical applications to composite materials and porous media. The discussion will include symbolic and numerical techniques for factorizing matrix functions across various classes. Topics will span mathematical modeling, computer simulations, bioinformatics, and industrial mathematics, offering insights into diverse realms of problem-solving methodologies.
10. Function Spaces and their Applications to Nonlinear Evolutional Equations
  • Organizers: Baoxiang Wang, Xiuqing Chen, Mitsuru Sugimoto, and Naohito Tomita
  • Description: This session will focus on recent progress in various Banach function spaces arising from harmonic analysis and their applications to nonlinear evolution equations, including but not limited to
    * Sobolev spaces, Besov spaces, modulation spaces, Wiener amalgam spaces.
    * Linear and nonlinear dispersive/hyperbolic equations, Navier stokes equations.
11. Fractional Calculus and Fractional Differential Equations
  • Organizers: Arran Fernandez, Yuri Luchko and Joel E. Restrepo
  • Description: This session is devoted to the mathematical study of fractional calculus, specifically integro-differential operators of fractional order and the associated integro-differential equations. Purely theoretical results as well as those with scientific applications are welcomed.
12. Generalized Functions and Applications
  • Organizers: Michael Kunzinger and Marko Nedeljkov
  • Description: The session will be devoted to theory and application of generalized functions, which comprise, among others, distributions, ultradistributions, hyperfunctions and algebras of generalized functions. Applications include, but are not restricted to, linear and nonlinear partial differential equations, asymptotic analysis, geometry, mathematical physics, stochastic processes, and harmonic analysis, both in theoretical and numerical aspects. The session is open to contributions on any aspect of generalized functions and their applications.
13. Harmonic Analysis and Partial Differential Equations
  • Organizers: Michael Ruzhansky and Jens Wirth
  • Description: The session will focus on the interplay between harmonic analysis, operator theory and applications to partial differential equations.
14. Integral Transforms and Reproducing Kernels
  • Organizer: Zouhaïr Mouayn
  • Description: The main goal of the IGITRK is to support scientific research activity, to develop scientific exchange and international collaboration in the field of integral transforms, reproducing kernels and related areas.
15. Inverse Problems and Artificial Intelligence
  • Organizer: Sergey Kabanikhin, Maktagali Bektemesov, Syrym Kassenov, Bektemessov Zholaman
  • Description: The purpose of this session is to unite outstanding scientists and young researchers working in the field of inverse and ill-posed problems of natural science, Artificial Intelligence (AI), biomedicine, finance and economics, Earth and life sciences, to exchange experiences, discuss new results and trends in the development of numerical methods for solving inverse problems and their application in practice.
16. Methods of Analysis in the Research of the Geometry of Pseudo-Euclidean Spaces and their Generalization
  • Organizers: Mikes Josef, Artykbaev Abdullaaziz, and Andrey Kostin
  • Description: The session is devoted to the geometric researches of manifolds and submanifolds of pseudo-Euclidean space, applications of analysis methods in the geometry of pseudo-Euclidean manifolds, semi-Euclidean spaces with a degenerate metric. Research on the geometry of Minkowski, isotropic and Galilean spaces and their applications are of particular interest.
17. Modern Problems of Fractional Order Differential Equations
  • Organizers: Sabir Umarov and Ravshan Ashurov
  • Description: Fractional order differential equations and systems play an important role in modern mathematical modeling and in solution of various problems in natural and social sciences and engineering. Rapid development of fractional calculus last several decades spawned an abundance of new theoretical ideas and practical applications of theory of fractional differential equations and their systems. This section will discuss modern advances in the field and new perspectives in the future.
18. Partial Differential Equations on Curved Spacetimes
  • Organizers: Anahit Galstyan, Makoto Nakamura, and Karen Yagdjian
  • Description: The session will discuss various problems for partial differential equations on curved spacetimes. The topics will include the representation and qualitative properties of the solutions of initial value and boundary value problems for linear and nonlinear PDEs in the curved spacetimes, global existence and blow up of the solutions, and numerical simulations, etc.
19. PDEs, Dynamical Systems and Nonlinear Analysis
  • Organizers: Emanuel Guariglia, and Anar T. Assanova
  • Description: This session is a follow-up of the SS134 – 14th AIMS on Dynamical Systems, Differential Equations, and Applications (Abu Dhabi, 16-20 December 2024). We focus our attention on problems of PDEs, nonlinear analysis and dynamical systems. More precisely, we intend to deal with the interconnection between these three research fields including pure results and applications. Our main goal is to bring together scholars working in PDEs, nonlinear analysis and dynamical systems, in order to report the newest progress, exchange ideas and forge new cooperation. The following is a non-exhaustive list of topics to be discussed in this session.
    • Wavelet methods for PDEs
    • Self-similar solutions
    • Analytical methods for PDEs
    • PDEs, Lyapunov functions and stability
    • Dynamical systems and fractal sets
    • Analysis on fractals
    • Topological and variational methods in nonlinear analysis
20. Pseudo Differential Operators
  • Organizer: Man Wah Wong
  • Description: This special session is on pseudo-differential operators understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
21. Quaternionic and Clifford Analysis
  • Organizers: Swanhild Bernstein, Uwe Kähler, and Irene Sabadini
  • Description: Quaternionic and Clifford analysis are higher dimensional analogues of complex function theory and represent a function theory in R^n. In the last years quaternionic and Clifford analysis spread into several different directions such as continuous and discrete theory, slice monogenic functions as well as new applications to various fields. This session aims to present recent advances in the field of continuous and Clifford analysis as well as its applications in numerical analysis of PDE’s, signal and image processing, operator theory, and physics to a broad audience.
22. Recent Advances in Analysis of Nonlinear Dispersive PDEs
  • Organizers: Adilbek Kairzhan and Dmitry Pelinovsky
  • Description: Dispersive PDEs arise as mathematical models, which describe realistic phenomenons happening in physics, engineering and other applied fields. Since many years ago, understanding the qualitative properties of solutions to dispersive PDEs attracted a lot of attention, and dispersive equations were studied extensively from both pure and computational points of view. This session is devoted to talks concerning recent progress in analytical and numerical study of dispersive PDEs. The topics will include well-posedness of nonlinear PDEs and stability of nonlinear waves, as well as applications of PDE theory to water waves and waves on graphs and branched networks.
23. Recent Progress in Functional Inequalities and Applications
  • Organizers: Tohru Ozawa,  Durvudkhan Suragan, and Nurgissa Yessirkegenov
  • Description: This session is devoted to original research presentations from all areas of pure and applied mathematics, provided they are concerned with functional inequalities and their numerous applications. 
24. Several Complex Analysis
  • Organizers: Guangbin Ren and Wei Wang
  • Description:This session focuses on all aspects related to the theory of Several Complex Variables. Special emphasise is given to Analysis and Geometry in the context of Several Complex Variables.
25. Wavelet theory and its Related Topics
  • Organizers: Keiko Fujita and Akira Morimoto
  • Description: The theory of the mathematics is important, but it is also important to apply it to real life. This session intends to discuss not only basic theoretical results on mathematics, especially wavelet analysis and Fourier analysis, but also the applied mathematics related to the research in engineering, medicine, acoustics,and the other various fields.
26. Contributed talks (open session)